Chapter 8: Q. 27 (page 541)

Find the area of the triangle. Round answer to two decimal places.
$A = 40 °, B = 20 °, a = 2$

Short Answer

Expert verified

The area of the triangle is 0.92 square units.

Step by step solution

Step 1. Given information.

The given values are:

$\begin{array}{rcl} A & = & 40 ° \\ B & = & 20 ° \\ a & = & 2 \end{array}$

Step 2. Determine the third angle.

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

$\begin{array}{rcl} A + B + C & = & 180 ° \\ 40 ° + 20 ° + C & = & 180 ° \\ C & = & 180 ° - 60 ° \\ C & = & 120 ° \end{array}$

Step 3. Determine the area of the triangle.

The area of a triangle is:

$K = \frac{a^{2} \sin B \sin C}{2 \sin A}$

Substitute the values in the above formula.

$\begin{array}{rcl} K & = & \frac{(2)^{2} \sin (20 °) \sin (120 °)}{2 \sin (40 °)} \\ K & = & \frac{4 (0.342) (0.866)}{2 (0.643)} \\ K & = & 0.921219 . . . \\ K & \approx & 0.92 \end{array}$

Step 4. Conclusion.

The area of the triangle is 0.92 square units.

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Find the area of the triangle. Round answer to two decimal places.
$A = 40 °, B = 20 °, a = 2$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the third angle.

Step 3. Determine the area of the triangle.

Step 4. Conclusion.

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Find the area of the triangle. Round answer to two decimal places.A=40°,B=20°,a=2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the third angle.

Step 3. Determine the area of the triangle.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Find the area of the triangle. Round answer to two decimal places.
$A = 40 °, B = 20 °, a = 2$